Over the Christmas holiday, the number of LEGO bricks in my house increased significantly. My son received LEGO sets as gifts from numerous grandparents, aunts and uncles. I was a LEGO fan when I was a child and now I have an excuse to play with them again as an adult. We've had lots of fun recently building sets and designing our own creations. At some point I became inspired to create a scale model of our home.

Planning and Building

I started this small project by building a test model to try out the proportions and to see what kinds of bricks I would need. The sizes of the door and window established the overall size. I continued revising the structure it until it looked right and then started collecting the bricks I needed.

Building this model reminded me of working on an OpenMiddle.com math problem. In an "open middle" problem, there is a one starting point and one solution but many different paths to get to the solution. With LEGO, there are many different ways to create, revise and improve your model. There are lots of different building techniques that will all result in a well designed scale model.

Scale

After I created my initial rough model I did some reading up on LEGO scale. It turns out that it is a fairly complex topic that lots of different people have investigated. I found the Brick Architect web site to be very helpful. For "classic minifigure" scale a ratio of 1:42 can be used. One major difficulty in discussing scale is that the proportions of a LEGO minifigure are not even close to the proportions of an actual person. A LEGO minifigure is about 4 cm tall and 1.6 cm wide. An average male human is about 175 cm tall and 40 cm wide... about half as wide as a minifigure would be at that height. Another challenge is converting units. The architectural drawings of my house are in feet, which I converted to metric (cm), then a scale factor is applied and finally the metric units are converted into LEGO bricks. I found an awesome tool that does this all for you, the LEGO Unit Converter.

Finance

I used a lot of estimation to determine how many bricks of each type I would need. LEGO bricks are not cheap so you don't want to order more than you need (Check out Jon Orr's activity involving cost, Is LEGO Gender Biased?). I purchased the bricks I needed on BrickLink.com, a large online LEGO marketplace. BrickLink provides a detailed price guide for every brick available which makes it really easy to know if you're getting a good deal or not.

I needed lots of 45 degree angle slope bricks for the roof of my house. These price stats let me know what a reasonable price is to pay for new or used bricks of this type. It is amazing to see how many bricks are sold on this site. I think that the stats from this site could make for an interesting grade 12 math research project.

The Finished Project

I only built the front 1/3 of the house for reasons of both space and cost. When I have time, I'll build this model virtually in the LEGO Digital Designer. This tool allows you to design LEGO models in a virtual 3D environment and quickly see the number of bricks used to create it. My son is enjoying our LEGO house and currently has his LEGO fire truck rescuing our LEGO cat from the roof. New adventures await!

Scale is a concept that is found at numerous grade levels in the Nova Scotia Mathematics curriculum. Scale drawings and models, similar polygons, and proportions are all found in mathematics outcomes. In math, scale is the ratio of the length in an image (or model) to the length of the actual object.

Below is a question relating to scale factors. A scale factor is the ratio of any two corresponding lengths in two similar geometric figures. Take a look at the three different versions of Connect Four. Estimate the scale factor between each pair of game boards from the given pictures. Estimate the radius of each of the coloured chips. Is the scale factor of the radius of each coloured chip the same as the scale factor of their volume? ​

Travel Size

Standard Size

Giant Size

You might ask students how scale is different from proportion. Try out this question: How big would a game board of Connect Four Hundred be (or even Connect Four Million) compared to Connect Four?

In visual arts, scale refers to the size ratio between objects within an image. Using a consistent scale will make a drawing look more realistic. Objects do not appear too large or too small when compared to each other. Sometimes however, an artist might intentionally change the scale of certain objects in an image. One such technique is called 'Hieratic scale' or sometimes 'Hierarchical proportion'. This technique can be seen in paintings and sculpture from the middle ages where powerful or holy people were sometimes painted larger than ordinary or less important people to show their relative importance. The larger a person was, the greater their importance.

The painting to the left is titled 'Saint Lawrence Enthroned with Saints and Donors.' It was painted by the Italian artist Fra Filippo Lippi in the fifteenth century. The central figure of this painting is Saint Lawrence who is significantly larger than all the other figures in the painting. He is flanked by Saints Cosmas and Damian who are slightly smaller. Smaller still, kneeling in the foreground, are members of the Alessandri family who commissioned this artwork. Using this hieratic scale, the artist quickly establishes Saint Lawrence as the focal point and also indicates the relative importance of the other figures.

Visual artists might also play with scale as it relates to perspective. One way to do this is called a Ponzo Illusion. The brain tends to judge an object's size by its background. Congruent object in different places on an image may appear to be different sizes. This is because of the cues the brain takes from linear perspective.

Which tree appears larger?

It would be fun to show students examples of how visual artists play with scale in order to make an impact on the viewer. Students might even be given an opportunity to create a piece of art that has an exaggerated or inconsistent scale or plays with forced perspective.

Nova Scotia Mathematics Curriculum OutcomesGrade 6 N05 - Students will be expected to demonstrate an understanding of ratio, concretely, pictorially, and symbolically. Grade 8 N04 - Students will be expected to demonstrate an understanding of ratio and rate.Grade 8 N05 - Students will be expected to solve problems that involve rates, ratios, and proportional reasoning.Grade 9 G03 - Students will be expected to draw and interpret scale diagrams of 2-D shapes. Math at Work 10 G03 - Students will be expected to demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.Mathematics Essentials 11 D9 - calculate scale factors in 2-D scale diagrams and 3-D scale models understand the relationship among the scale factor and the related change in area or volume.Math at Work 11 G02 - Students will be expected to solve problems that involve scale.Mathematics 11 M03 - Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects.

The Discovery Centre is a hands-on science centre in downtown Halifax. My almost 5 year old son and I has visited on numerous occassions. On my most recent visit, my son spent some time building with Lego bricks in the Lindsay Construction Building Centre. While he played, I took a closer look at the Lego replica Town Clock that sits nearby. What would students notice or wonder about given a picture of this model? There is a fantastic sign on the wall behind the model that lists exactly how many Lego bricks of each colour were used in its construction.

Here are a few questions that I thought about:

Does the amount of visible colour help you determine the number of bricks of each colour used to build this model? Since the Lego bricks used are of various sizes, I think estimating the number of bricks (especially white bricks) from the image would be challenging. Perhaps comparing this building to a Lego kit with a know number of pieces (such as the Lego Town Hall) might help.

If I told you that there were about twice as many green bricks as grey bricks, would that help you estimate the number of bricks?

If I told you that this model was build with 12,465 Lego bricks, how many of those bricks would you estimate are white bricks?

Given the number of bricks used, how long do you think it took to build this model?

What is the scale of the model to the actual Town Clock? How precise do you think this scale model is?

Given the list of lego bricks, you could ask students a number of additional questions:

For each different colour of Lego brick, what fraction (or percentage) of the whole model is it? What is the exact fraction and what is the best simple approximation (using a single digit in the numerator).

Can you find two different sets of colours that have similar ratios? Which two sets of colours have the closets ratios?

If you reduced the scale of this model in half, about how many of each color brick would you expect to use?

The Discovery Centre is currently working on a project to build Canada's largest Lego mosaic wall. The wall will be installed at the Discovery Centre's new location when it moves.

Nova Scotia Mathematics Curriculum Outcomes Mathematics 7 - N07 Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals. Mathematics 8 - N03 Students will be expected to demonstrate an understanding of and solve problems involving percents greater than or equal to 0%.Mathematics 8 - N04 Students will be expected to demonstrate an understanding of ratio and rate.Mathematics 9 - N03 Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.Mathematics at Work 11 - G02 Students will be expected to solve problems that involve scale.